Least Common Multiple (LCM) of 143 and 75
The least common multiple (LCM) of 143 and 75 is 10725.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 143 and 75?
First, calculate the GCD of 143 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 75 = 1 remainder 68 |
| 2 | 75 ÷ 68 = 1 remainder 7 |
| 3 | 68 ÷ 7 = 9 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 98 | 9800 |
| 98 and 80 | 3920 |
| 152 and 89 | 13528 |
| 26 and 148 | 1924 |
| 191 and 39 | 7449 |